The simple example of styling DatePicker (only single & multiple mode)

DatePicker.vue

<template>
  <div id="app">
      <v-calendar title-position="right" :formats="forDatePicker" :attributes="action"></v-calendar>
      <v-date-picker mode="single" :attributes="action" v-model="action[0].dates" :formats="forDatePicker"></v-date-picker>
  </div>
</template>

<script>
import Vue from 'vue'
import VCalendar from 'v-calendar'
import 'v-calendar/lib/v-calendar.min.css'

Vue.use(VCalendar, {
  firstDayOfWeek: 2,
  locale: 'en-US',
  titleTransition: 'slide-v',
  weeksTransition: 'fade',
  datePickerTintColor: '#1ebb42',
  datePickerShowCaps: true
});

export default {
  name: 'app',
  data() {
    return {
      options: {
        animated: !0,
        backgroundColor: 'white',
        color: "black",
        height: "1.8rem",
        borderWidth: "4px",
        borderStyle: "solid",
        borderRadius: "5px",
        opacity: 1
      },
      forDatePicker: {
        title: 'MMM of YYYY',
        navMonths: 'MMM',
        weekdays: 'WWW',
        input: ['YYYY/MM/DD', 'YYYY/MM/D', 'YYYY-MM-DD'],
        dayPopover: 'Do of MMMM',
        data: ['YYYY-MM-DD', 'YYYY/MM/DD']
      },
      action: [
        {
          key: 'today',
          highlight: {
            backgroundColor: '#1ebb42',
            borderRadius: '5px',
 	          borderColor: '#1ebb42',
            borderWidth: '4px'
          },
          contentStyle: {
            color: '#fff',
            borderWidth: '4px',
            borderRadius: '5px'
          },
          dates: [new Date('2018/10/17'), new Date(), new Date('2018/10/21')]
        }
      ]
    }
  },
  created() {
    console.log(this.action[0].dates);
  }
}
</script>